Question

The graph of polynomial $P(x) = ax - b$, where $a \ne 0$; $a,b \in R$ intersect X-axis at
A. $\left( {\dfrac{b}{a},0} \right)$
B. $\left( {0,\dfrac{b}{a}} \right)$
C. $\left( { - \dfrac{b}{a},0} \right)$
D. $\left( { - \dfrac{a}{b},0} \right)$

Answer 1

Hint: Here we will find the point of intersection of the polynomial at X-axis i.e., by using P(x) =0.

Complete step-by-step answer:

Here we have to tell the coordinate at which the graph of polynomial $P(x) = ax - b$ cuts the x-axis.
Now when this polynomial cuts the x-axis $P(x) = 0$ hence
$
  ax - b = 0 \\
  \Rightarrow {\text{ x = }}\dfrac{b}{a} \\
$
Now for the x-axis y coordinate is always zero so we can say that the point at which this polynomial intersects the x axis will be $(\dfrac{b}{a},0)$.
Hence option (A) is the correct option.

Note: Whenever we were being told to tell the points where the polynomial cuts the x-axis means that we were being told to find the zeros of the polynomial hence we simply need to put it equal to zero to obtain desired points.